{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 0.补充\n",
    "在介绍高斯混合模型的变分推断之前先补充两个分布的知识，一个是高斯-Wishart分布，它是高维高斯分布的共轭先验，另一个是学生t分布，它是高斯-Gamma分布对精度积分的边缘概率分布，下面分别介绍\n",
    "\n",
    "#### 高斯-Wishart分布\n",
    "\n",
    "对于$D$维向量$x$的多元高斯分布$N(x\\mid\\mu,\\Lambda^{-1})$，假设精度$\\Lambda$已知，则均值$\\mu$的共轭先验分布仍为高斯分布，但对于均值已知，精度未知的情况，其共轭先验是Wishart分布，定义如下：   \n",
    "\n",
    "$$\n",
    "\\mathcal{W}(\\Lambda\\mid W,\\mathcal{v})=B|\\Lambda|^{\\frac{\\mathcal{v}-D-1}{2}}exp(-\\frac{1}{2}Tr(W^{-1}\\Lambda))\n",
    "$$  \n",
    "\n",
    "其中，$\\mathcal{v}$被称为分布的自由度数量，$W$是一个$D\\times D$的标量矩阵，$Tr(\\cdot)$表示矩阵的迹，归一化系数$B$为：  \n",
    "\n",
    "$$\n",
    "B(W,\\mathcal{v})=|W|^{-\\frac{\\mathcal{v}}{2}}(2^{\\frac{\\mathcal {v}D}{2}}\\pi^{\\frac{D(D-1)}{4}}\\prod_{i=1}^D\\Gamma(\\frac{\\mathcal{v}+1-i}{2}))^{-1}\n",
    "$$  \n",
    "\n",
    "而对于均值和精度均未知的情况，那么类似于一元变量的推理方法，可以得到其共轭先验为：   \n",
    "\n",
    "$$\n",
    "p(\\mu,\\Lambda\\mid\\mu_0,beta,W,\\mathcal{v})=N(\\mu\\mid\\mu_0,(\\beta\\Lambda)^{-1})\\mathcal{W}(\\Lambda\\mid W,\\mathcal{v})\n",
    "$$  \n",
    "\n",
    "该分布便是高斯-Wishart分布，或者正态-Wishart分布\n",
    "\n",
    "#### 学生t分布\n",
    "根据之前的推导我们知道，对于$\\mu$已知，$\\tau$未知的一元高斯分布$N(x\\mid\\mu,\\tau^{-1})$，它的共轭分布为Gamma分布，不妨表示为$Gam(\\tau\\mid a,b)$，如果把精度积分掉，那么就得到了一个边缘概率分布：   \n",
    "\n",
    "$$\n",
    "p(x\\mid \\mu,a,b)=\\int_0^\\infty N(x\\mid\\mu,\\tau^{-1})Gam(\\tau\\mid a,b)d\\tau\\\\\n",
    "=\\int_0^\\infty \\frac{b^ae^{(-b\\tau)}\\tau^{a-1}}{\\Gamma(a)}(\\frac{\\tau}{2\\pi})^{\\frac{1}{2}}exp(-\\frac{\\tau}{2}(x-\\mu)^2)d\\tau\\\\\n",
    "=\\frac{b^a}{\\Gamma(a)}(\\frac{1}{2\\pi})^{\\frac{1}{2}}\\int_0^\\infty(\\frac{z}{b+\\frac{(x-\\mu)^2}{2}})^{a-\\frac{1}{2}}e^{-z}[b+\\frac{(x-\\mu)^2}{2}]^{-1}dz（令z=\\tau(b+\\frac{(x-\\mu)^2}{2})）\\\\\n",
    "=\\frac{b^a}{\\Gamma(a)}(\\frac{1}{2\\pi})^{\\frac{1}{2}}(b+\\frac{(x-\\mu)^2}{2})^{-a-\\frac{1}{2}}\\int_0^\\infty z^{(a+\\frac{1}{2})-1}e^{-z}dz\\\\\n",
    "=\\frac{b^a}{\\Gamma(a)}(\\frac{1}{2\\pi})^{\\frac{1}{2}}(b+\\frac{(x-\\mu)^2}{2})^{-a-\\frac{1}{2}}\\Gamma(a+\\frac{1}{2})\n",
    "$$  \n",
    "\n",
    "我们对参数做一下调整，令$\\mathcal{v}=2a,\\lambda=\\frac{a}{b}$，那么这就是学生t分布：   \n",
    "\n",
    "$$\n",
    "St(x\\mid\\mu,\\lambda,\\mathcal{v})=\\frac{\\Gamma(\\frac{\\mathcal{v}}{2}+\\frac{1}{2})}{\\Gamma(\\frac{\\mathcal{v}}{2})}(\\frac{\\lambda}{\\pi\\mathcal{v}})^{\\frac{1}{2}}(1+\\frac{\\lambda(x-\\mu)^2}{\\mathcal{v}})^{-\\frac{\\mathcal{v}}{2}-\\frac{1}{2}}\n",
    "$$  \n",
    "\n",
    "这里，参数$\\lambda$被称为t分布的精度（注意：通常情况下，它不是方差的倒数），参数$\\mathcal{v}$被称为自由度，它的作用如下图所示（其中$\\mu=0,\\lambda=1$），对于$\\mathcal{v}=1$的情况下，t分布是柯西分布，而对于$\\mathcal{v}\\rightarrow \\infty$的情况下，t分布$St(x\\mid\\mu,\\lambda,\\mathcal{v})$就变成了高斯分布$N(x\\mid\\mu,\\lambda^{-1})$   \n",
    "\n",
    "\n",
    "![avatar](./source/15_t分布1.png)\n",
    "\n",
    "需要注意的一点是，学生t分布可以看作无限个同均值不同精度的高斯分布相加所得到（高斯混合模型的极限），所以t分布通常有更长的“尾巴”，建模时具有更强的鲁棒性，如下图是用t分布（红线）和高斯分布（绿线）建模的对比，在未引入噪声数据之前，如（a）图，t分布和高斯分布的建模效果相同，而在引入噪声数据之后，如（b）图，会对高斯分布模型造成较大的影响，而t分布几乎不受影响\n",
    "\n",
    "![avatar](./source/15_t分布2.png)  \n",
    "\n",
    "\n",
    "高维学生t分布：   \n",
    "\n",
    "将一维学生t分布扩展到高维，可以写作  \n",
    "\n",
    "$$\n",
    "St(x\\mid\\mu,\\Lambda,\\mathcal{v})=\\frac{\\Gamma(\\frac{D}{2}+\\frac{\\mathcal{v}}{2})}{\\Gamma(\\frac{\\mathcal{v}}{2})}\\frac{|\\Lambda|^{\\frac{1}{2}}}{(\\pi\\mathcal{v})^{\\frac{D}{2}}}[1+\\frac{(x-\\mu)^T\\Lambda(x-\\mu)}{\\mathcal{v}}]^{-\\frac{D}{2}-\\frac{\\mathcal{v}}{2}}\n",
    "$$\n",
    "\n",
    "其中，$D$是$x$的维度，另外t分布具有如下的性质：   \n",
    "\n",
    "（1）$E[x]=\\mu,\\mathcal{v}>1$；   \n",
    "\n",
    "（2）$cov[x]=\\frac{\\mathcal{v}}{\\mathcal{v}-2}\\Lambda^{-1},\\mathcal{v}>2$；   \n",
    "\n",
    "（3）$mode[x]=\\mu$   \n",
    "\n",
    "好的，补充内容差不多就是这些了，接下来按照上一节总结的四个步骤来介绍高斯混合模型的变分推断"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 一.联合概率分布\n",
    "高斯混合模型的图模型如下图\n",
    "![avatar](./source/15_VI_GMM1.png)\n",
    "\n",
    "这里是概率图的盘式记法，其中，紫色实心的圈表示观测变量，红色空心圈表示隐变量（参数），框（盘子）内表示$N$次独立同分布的观测，接下来首先从似然函数出发，对于我们的每个观测$x_n$，都有一个对应的隐变量$z_n$，它是一个$K$维的二值向量，每个元素为$z_{nk},k=1,2,...,K$，表示对应的观测$x_n$是否采样于第$k$个高斯分布，对于给定的混合系数$\\pi=\\{\\pi_1,\\pi_2,...,\\pi_K\\}$（即每个高斯分布的权重系数），可以写出$Z={z_1,z_2,...,z_N}$关于$\\pi$的条件概率分布：   \n",
    "\n",
    "$$\n",
    "p(Z\\mid\\pi)=\\prod_{n=1}^N\\prod_{k=1}^K\\pi_k^{z_{nk}}\n",
    "$$  \n",
    "\n",
    "同样地，在给定了$Z,\\mu,\\Lambda=\\Sigma^{-1}$的条件下，我们可以写出观测数据的条件概率分布：   \n",
    "\n",
    "$$\n",
    "p(X\\mid Z,\\mu,\\Lambda)=\\prod_{n=1}^N\\prod_{k=1}^KN(x_n\\mid\\mu_k,\\Lambda_k^{-1})^{z_{nk}}\n",
    "$$  \n",
    "\n",
    "这里，$\\mu=\\{\\mu_k\\},\\Lambda=\\{\\Lambda_k\\}$，这里使用精度矩阵是为了后面的计算方便，接下来引入参数$\\mu,\\Lambda,\\pi$上的先验概率分布，显然为了计算简单，我们可以使用共轭先验，对于混合系数$\\pi$的先验概率，我们可以使用狄利克雷分布：   \n",
    "\n",
    "$$\n",
    "p(\\pi)=Dir(\\pi\\mid\\alpha_0)=C(\\alpha_0)\\prod_{k=1}^K\\pi_k^{\\alpha_0-1}\n",
    "$$  \n",
    "\n",
    "这里，我们假设每个高斯分布的被观测的先验数量都一样为$\\alpha_0$，$C(\\alpha_0)$表示归一化系数，而对于$\\mu,\\Lambda$可以选择高斯-Wishart先验分布：  \n",
    "\n",
    "$$\n",
    "p(\\mu,\\Lambda)=p(\\mu\\mid\\Lambda)p(\\Lambda)\\\\\n",
    "=\\prod_{k=1}^KN(\\mu_k\\mid m_0,(\\beta_0\\Lambda_k)^{-1})\\mathcal{W}(\\Lambda_k\\mid W_0,\\mathcal{v}_0)\n",
    "$$  \n",
    "\n",
    "为了对称性，通常取$m_0=0$，注意，由于高斯-Wishart分布中$\\mu$的概率分布的方差是$\\Lambda$的函数，所以，这时的概率图模型需要被更新为如下形式：  \n",
    "![avatar](./source/15_VI_GMM2.png)  \n",
    "\n",
    "根据概率图模型，我们将上面的几项乘起来就是联合概率分布咯：   \n",
    "\n",
    "$$\n",
    "p(X,Z,\\pi,\\mu,\\Lambda)=p(X\\mid Z,\\mu,\\Lambda)p(Z\\mid\\pi)p(\\pi)p(\\mu\\mid\\Lambda)p(\\Lambda)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 二.变分分布\n",
    "上面推导出了联合概率分布，那么接下来就需要造一个变分分布去近似它的后验概率分布咯：   \n",
    "\n",
    "$$\n",
    "q(Z,\\pi,\\mu,\\Lambda)\\rightarrow p(Z,\\pi,\\mu,\\Lambda\\mid X)\n",
    "$$   \n",
    "\n",
    "接下来，我们做一个假设：变分分布可以在隐变量和参数之间记性分解，即：   \n",
    "\n",
    "$$\n",
    "q(Z,\\pi,\\mu,\\Lambda)=q(Z)q(\\pi,\\mu,\\Lambda)\n",
    "$$  \n",
    "\n",
    "注意，这里省略了下标，$q(Z)$与$q(\\pi,\\mu,\\Lambda)$是不一样的分布，我们通过参数来区分不同的分布，接下来，就有：   \n",
    "\n",
    "$$\n",
    "ln\\ q^*(Z)=E_{\\pi,\\mu,\\Lambda}[ln\\ p(X,Z,\\pi,\\mu,\\Lambda)]+const\n",
    "$$  \n",
    "\n",
    "将上面，联合概率分布的表达式带入可得（将与$Z$无关的项整合到$const$中）：   \n",
    "\n",
    "$$\n",
    "ln\\ q^*(Z)=E_\\pi[ln\\ p(Z\\mid\\pi)]+E_{\\mu,\\Lambda}[ln\\ p(X\\mid Z,\\mu,\\Lambda)]+const\n",
    "$$  \n",
    "\n",
    "替换右侧的两个条件分布，然后再次把与$Z$无关的项整合到$const$中：   \n",
    "\n",
    "$$\n",
    "ln\\ q^*(Z)=\\sum_{n=1}^N\\sum_{k=1}^Kz_{nk}ln\\ \\rho_{nk}+const\n",
    "$$  \n",
    "\n",
    "其中：  \n",
    "$$\n",
    "ln\\ \\rho_{nk}=E[ln\\ \\pi_k]+\\frac{1}{2}E[ln\\ |\\Lambda_k|]-\\frac{D}{2}ln(2\\pi)-\\frac{1}{2}E_{\\mu_k,\\Lambda_k}[(x_n-\\mu_k)^T\\Lambda_k(x_n-\\mu_k)]\n",
    "$$   \n",
    "\n",
    "其中，$D$是观测变量$x$的维度，对上面的等式两边取指数，有：   \n",
    "\n",
    "$$\n",
    "q^*(Z)\\propto\\prod_{n=1}^N\\prod_{k=1}^K\\rho_{nk}^{z_{nk}}\n",
    "$$  \n",
    "\n",
    "由于，$q^*(Z)$需要是归一化的，而且同时$z_{nk},k=1,2,...,K$是二值的（$K$个数中只有一个为1，其余为0），所以，我们有：   \n",
    "\n",
    "$$\n",
    "q^*(Z)=\\prod_{n=1}^N\\prod_{k=1}^Kr_{nk}^{z_{nk}}\\\\\n",
    "r_{nk}=\\frac{\\rho_{nk}}{\\sum_{j=1}^K\\rho_{nj}}\n",
    "$$  \n",
    "\n",
    "对于离散情况有：   \n",
    "\n",
    "$$\n",
    "E[z_{nk}]=r_{nk}\n",
    "$$  \n",
    "\n",
    "可以发现，$q^*(Z)$的最优解是依赖于其他变量的，即它们是耦合的，需要使用迭代的方式进行求解，为了后面的推导方便，我们定义如下的三个量：   \n",
    "\n",
    "$$\n",
    "N_k=\\sum_{n=1}^Nr_{nk}\\\\\n",
    "\\bar{x}_k=\\frac{1}{N_k}\\sum_{n=1}^Nr_{nk}x_n\\\\\n",
    "S_k=\\frac{1}{N_k}\\sum_{n=1}^Nr_{nk}(x_n-\\bar{x}_k)(x_n-\\bar{x}_k)^T\n",
    "$$  \n",
    "\n",
    "大家可以发现，这里定义的这些量其实和EM算法中计算用到的量类似，接下来看看$q(\\pi,\\mu,\\Lambda)$：   \n",
    "\n",
    "$$\n",
    "ln\\ q^*(\\pi,\\mu,\\Lambda)=ln\\ p(\\pi)+\\sum_{k=1}^Kln\\ p(\\mu_k,\\Lambda_k)+E_Z[ln\\ p(Z\\mid\\pi)]+\\sum_{k=1}^K\\sum_{n=1}^NE[z_{nk}]ln\\ N(x_n\\mid\\mu_k,\\Lambda_k^{-1})+const\n",
    "$$  \n",
    "\n",
    "可以发现，表达式右边中一些项只与$\\pi$相关，另外一些项只与$\\mu$和$\\Lambda$相关，也就是说$q(\\pi,\\mu,\\Lambda)$还可以进一步分解为$q(\\pi)q(\\mu,\\Lambda)$，而$q(\\mu,\\Lambda)$由可以分解为$k$与$\\mu_k,\\Lambda_k$相关的项，所以：   \n",
    "\n",
    "$$\n",
    "q(\\pi,\\mu,\\Lambda)=q(\\pi)\\prod_{k=1}^Kq(\\mu_k,\\Lambda_k)\n",
    "$$  \n",
    "\n",
    "分离出与$\\pi$相关的项，我们有：   \n",
    "\n",
    "$$\n",
    "ln\\ q^*(\\pi)=(\\alpha_0-1)\\sum_{k=1}^Kln\\ \\pi_k+\\sum_{k=1}^K\\sum_{n=1}^Nr_{nk}ln\\ \\pi_k+const\n",
    "$$  \n",
    "\n",
    "对上面的表达式两侧取指数可以发现，$q^*(\\pi)$是一个狄利克雷分布：   \n",
    "\n",
    "$$\n",
    "q^*(\\pi)=Dir(\\pi\\mid\\alpha),\\alpha_k=\\alpha_0+N_k\n",
    "$$    \n",
    "\n",
    "最后，我们可以推出$q^*(\\mu_k,\\Lambda_k)$是一个高斯-Wishart分布：   \n",
    "\n",
    "$$\n",
    "q^*(\\mu_k,\\Lambda_k)=N(\\mu_k\\mid m_k,(\\beta_k\\Lambda_k)^{-1})\\mathcal{W}(\\Lambda_k\\mid W_k,\\mathcal{v}_k)\n",
    "$$   \n",
    "\n",
    "其中：   \n",
    "\n",
    "$$\n",
    "\\beta_k=\\beta_0+N_k\\\\\n",
    "m_k=\\frac{1}{\\beta_k}(\\beta_0m_0+N_k\\bar{x}_k)\\\\\n",
    "W_k^{-1}=W_0^{-1}+N_kS_k+\\frac{\\beta_0N_k}{\\beta_0+N_k}(\\bar{x}_k-m_0)(\\bar{x}_k-m_0)^T\\\\\n",
    "\\mathcal{v}_k=\\mathcal{v}_0+N_k\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 三.迭代更新\n",
    "\n",
    "根据上面的推导，迭代更新流程就知道了：$r_{nk}\\rightarrow \\pi_k,\\mu_k,\\Lambda_k\\rightarrow r_{nk}\\rightarrow \\cdots$，剩余还需要进一步求解的便是$r_{nk}$被归一化前的变量$\\rho_{nk}$，它的计算公式，我们再写一下：   \n",
    "\n",
    "$$\n",
    "ln\\ \\rho_{nk}=E[ln\\ \\pi_k]+\\frac{1}{2}E[ln\\ |\\Lambda_k|]-\\frac{D}{2}ln(2\\pi)-\\frac{1}{2}E_{\\mu_k,\\Lambda_k}[(x_n-\\mu_k)^T\\Lambda_k(x_n-\\mu_k)]\n",
    "$$  \n",
    "\n",
    "根据Wishart分布，狄利克雷分布的特性，我们可以得到：   \n",
    "\n",
    "$$\n",
    "E[ln\\ |\\Lambda_k|]=\\sum_{i=1}^D\\psi(\\frac{\\mathcal{v}_k+1-i}{2})+Dln2+ln|W_k|\\\\\n",
    "E[ln\\ \\pi_k]=\\psi(\\alpha_k)-\\psi(\\hat{\\alpha})\n",
    "$$   \n",
    "\n",
    "这里$\\hat{\\alpha}=\\sum_k\\alpha_k$，$\\psi(\\cdot)$表示Digamma函数：   \n",
    "$$\n",
    "\\psi(a)=\\frac{d}{da}ln\\Gamma(a)\n",
    "$$  \n",
    "\n",
    "另外，由高斯-Wishart分布，可以求得：   \n",
    "\n",
    "\n",
    "$$\n",
    "E_{\\mu_k,\\Lambda_k}[(x_n-\\mu_k)^T\\Lambda_k(x_n-\\mu_k)]=D\\beta_k^{-1}+\\mathcal{v}_k(x_n-m_k)^TW_k(x_n-m_k)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 四.变分分布的应用：概率密度预测\n",
    "对于GMM，我们通常对新样本$\\hat{x}$的概率密度感兴趣，根据贝叶斯推断理论，它的预测过程可以写作：   \n",
    "\n",
    "$$\n",
    "p(\\hat{x}\\mid X)=\\sum_{\\hat{z}}\\int\\int\\int p(\\hat{x}\\mid \\hat{z},\\mu,\\Lambda)p(\\hat{z}\\mid \\pi)p(\\pi,\\mu,\\Lambda\\mid X)d\\pi d\\mu d\\Lambda\\\\\n",
    "=\\sum_{k=1}^K\\int\\int\\int \\pi_kN(\\hat{x}\\mid \\mu_k,\\Lambda_k^{-1})p(\\pi,\\mu,\\Lambda\\mid X)d\\pi d\\mu d\\Lambda（消去\\hat{x}）\\\\\n",
    "\\simeq \\sum_{k=1}^K\\int\\int\\int \\pi_kN(\\hat{x}\\mid \\mu_k,\\Lambda_k^{-1})q(\\pi)q(\\mu_k,\\Lambda_k)d\\pi d\\mu_k d\\Lambda_k（变分分布替换后验分布）\\\\\n",
    "=\\frac{1}{\\hat{\\alpha}}\\sum_{k=1}^K\\alpha_kSt(\\hat{x}\\mid m_k,L_k,\\mathcal{v}_k+1-D)\n",
    "$$  \n",
    "\n",
    "我们最终发现，概率密度其实是学生t分布的混合，其中：   \n",
    "\n",
    "$$\n",
    "L_k=\\frac{(\\mathcal{v}_k+1-D)\\beta_k}{1+\\beta_k}W_k\n",
    "$$  \n",
    "\n",
    "各符号的意义与前面推导的一致"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 五.代码实现\n",
    "首先，我们将几个分布的函数写一下"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import special\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "代码封装到utils中\n",
    "\"\"\"\n",
    "\n",
    "def dirichlet(u, alpha):\n",
    "    \"\"\"\n",
    "    狄利克雷分布\n",
    "    :param u: 随机变量\n",
    "    :param alpha: 超参数\n",
    "    :return:\n",
    "    \"\"\"\n",
    "    # 计算归一化因子\n",
    "    beta = special.gamma(np.sum(alpha))\n",
    "    for alp in alpha:\n",
    "        beta /= special.gamma(np.sum(alp))\n",
    "    rst = beta\n",
    "    # 计算结果\n",
    "    for idx in range(0, len(alpha)):\n",
    "        rst *= np.power(u[idx], alpha[idx] - 1)\n",
    "    return rst\n",
    "\n",
    "\n",
    "def wishart(Lambda, W, v):\n",
    "    \"\"\"\n",
    "    wishart分布\n",
    "    :param Lambda:随机变量\n",
    "    :param W:超参数\n",
    "    :param v:超参数\n",
    "    :return:\n",
    "    \"\"\"\n",
    "    # 维度\n",
    "    D = W.shape[0]\n",
    "    # 先计算归一化因子\n",
    "    B = np.power(np.linalg.det(W), -1 * v / 2)\n",
    "    B_ = np.power(2.0, v * D / 2) * np.power(np.pi, D * (D - 1) / 4)\n",
    "    for i in range(1, D + 1):\n",
    "        B_ *= special.gamma((v + 1 - i) / 2)\n",
    "    B = B / B_\n",
    "    # 计算剩余部分\n",
    "    rst = B * np.power(np.linalg.det(Lambda), (v - D - 1) / 2)\n",
    "    rst *= np.exp(-0.5 * np.trace(np.linalg.inv(W) @ Lambda))\n",
    "    return rst\n",
    "\n",
    "\n",
    "def St(X, mu, Lambda, v):\n",
    "    \"\"\"\n",
    "    学生t分布\n",
    "    :param X: 随机变量\n",
    "    :param mu: 超参数\n",
    "    :param Lambda: 超参数\n",
    "    :param v: 超参数\n",
    "    :return:\n",
    "    \"\"\"\n",
    "    n_sample, D = X.shape\n",
    "    return special.gamma(D / 2 + v / 2) * np.power(np.linalg.det(Lambda), 0.5) * np.power(\n",
    "        1 + np.sum((X - mu) @ Lambda * (X - mu), axis=1) / v, -1.0 * D / 2 - v / 2) / special.gamma(v / 2) / np.power(\n",
    "        np.pi * v, D / 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下里就是模型代码了..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.chdir('../')\n",
    "from ml_models import utils\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "高斯混合模型的变分推断实现，封装到ml_models.vi中\n",
    "\"\"\"\n",
    "\n",
    "\n",
    "class GMMCluster(object):\n",
    "    def __init__(self, n_components=1, tol=1e-6, n_iter=100, prior_dirichlet_alpha=None, prior_gaussian_mean=None,\n",
    "                 prior_gaussian_beta=None, prior_wishart_w=None, prior_wishart_v=None,\n",
    "                 verbose=False):\n",
    "        \"\"\"\n",
    "        GMM的VI实现\n",
    "        :param n_components: 高斯混合模型数量\n",
    "        :param tol: -log likehold增益<tol时，停止训练\n",
    "        :param n_iter: 最多迭代次数\n",
    "        :prior_dirichlet_alpha:先验狄利克雷分布的超参数\n",
    "        :prior_gaussian_mean:先验高斯分布的均值\n",
    "        :prior_gaussian_beta:先验高斯分布的beta值，即精度前的系数\n",
    "        :prior_wishart_w:先验wishart分布的w\n",
    "        :prior_wishart_v:先验wishart分布的v\n",
    "        :param verbose: 是否可视化训练过程\n",
    "        \"\"\"\n",
    "        self.n_components = n_components\n",
    "        self.tol = tol\n",
    "        self.n_iter = n_iter\n",
    "        self.verbose = verbose\n",
    "        self.prior_dirichlet_alpha = prior_dirichlet_alpha\n",
    "        self.prior_gaussian_mean = prior_gaussian_mean\n",
    "        self.prior_gaussian_beta = prior_gaussian_beta\n",
    "        self.prior_wishart_w = prior_wishart_w\n",
    "        self.prior_wishart_v = prior_wishart_v\n",
    "        # 填充默认值\n",
    "        if self.prior_dirichlet_alpha is None:\n",
    "            self.prior_dirichlet_alpha_0 = np.asarray([1] * n_components)\n",
    "        self.prior_dirichlet_alpha = self.prior_dirichlet_alpha_0 + np.random.random(size=n_components) * 0.1\n",
    "        if self.prior_gaussian_beta is None:\n",
    "            self.prior_gaussian_beta_0 = np.asarray([1] * n_components)\n",
    "        self.prior_gaussian_beta = self.prior_gaussian_beta_0 + np.random.random(size=n_components) * 0.1\n",
    "\n",
    "        # 高斯模型参数\n",
    "        self.params = []\n",
    "        # 记录数据维度\n",
    "        self.D = None\n",
    "\n",
    "    def _init_params(self):\n",
    "        \"\"\"\n",
    "        初始化另一部分参数\n",
    "        :return:\n",
    "        \"\"\"\n",
    "        if self.prior_gaussian_mean is None:\n",
    "            self.prior_gaussian_mean_0 = np.zeros(shape=(self.n_components, self.D))\n",
    "        self.prior_gaussian_mean = self.prior_gaussian_mean_0 + np.random.random(\n",
    "            size=(self.n_components, self.D)) * 0.1\n",
    "        if self.prior_wishart_w is None:\n",
    "            self.prior_wishart_w_0 = [np.identity(self.D)] * self.n_components  # 单位矩阵\n",
    "        self.prior_wishart_w = []\n",
    "        for w in self.prior_wishart_w_0:\n",
    "            self.prior_wishart_w.append(w + np.random.random(size=(self.D, self.D)) * 0.1)\n",
    "\n",
    "        if self.prior_wishart_v is None:\n",
    "            self.prior_wishart_v_0 = np.asarray([self.D] * self.n_components)\n",
    "        self.prior_wishart_v = self.prior_wishart_v_0 + np.random.random(size=self.n_components) * 0.1\n",
    "\n",
    "    def _update_single_step(self, X):\n",
    "        # 首先计算3个期望\n",
    "        E_ln_Lambda = []\n",
    "        for k in range(0, self.n_components):\n",
    "            value = self.D * np.log(2) + np.log(np.linalg.det(self.prior_wishart_w[k]))\n",
    "            for i in range(1, self.D + 1):\n",
    "                value += utils.special.digamma((self.prior_wishart_v[k] + 1 - i) / 2)\n",
    "            E_ln_Lambda.append(value)\n",
    "        E_ln_pi = []\n",
    "        hat_alpha = np.sum(self.prior_dirichlet_alpha)\n",
    "        for k in range(0, self.n_components):\n",
    "            E_ln_pi.append(utils.special.digamma(self.prior_dirichlet_alpha[k]) - utils.special.digamma(hat_alpha))\n",
    "        E_mu_Lambda = []\n",
    "        for k in range(0, self.n_components):\n",
    "            value = self.D * (1.0 / self.prior_gaussian_beta[k]) + np.sum(self.prior_wishart_v[k] * (\n",
    "                X - self.prior_gaussian_mean[k]) @ self.prior_wishart_w[k] * (X - self.prior_gaussian_mean[k]), axis=1)\n",
    "            E_mu_Lambda.append(value)\n",
    "        # 然后计算 r_nk\n",
    "        rho_n_k = []\n",
    "        for k in range(0, self.n_components):\n",
    "            value = np.exp(E_ln_pi[k] + 0.5 * E_ln_Lambda[k] - self.D / 2.0 * np.log(2 * np.pi) - 0.5 * E_mu_Lambda[k])\n",
    "            rho_n_k.append(value)\n",
    "        rho_n_k = np.asarray(rho_n_k).T\n",
    "        r_n_k = rho_n_k / np.sum(np.asarray(rho_n_k), axis=1, keepdims=True)\n",
    "\n",
    "        # 然后计算N_k,\\bar{x}_k,S_k\n",
    "        N_k = np.sum(r_n_k, axis=0)\n",
    "        x_k = []\n",
    "        for k in range(0, self.n_components):\n",
    "            x_k.append(np.sum(r_n_k[:, [k]] * X, axis=0) / N_k[k])\n",
    "        S_k = []\n",
    "        for k in range(0, self.n_components):\n",
    "            S_k.append(np.transpose(r_n_k[:, [k]] * (X - x_k[k])) @ (r_n_k[:, [k]] * (X - x_k[k])) / N_k[k])\n",
    "\n",
    "        # 最后更新变分分布中的各个参数\n",
    "        for k in range(0, self.n_components):\n",
    "            self.prior_dirichlet_alpha[k] = self.prior_dirichlet_alpha_0[k] + N_k[k]\n",
    "\n",
    "            self.prior_gaussian_beta[k] = self.prior_gaussian_beta_0[k] + N_k[k]\n",
    "\n",
    "            self.prior_gaussian_mean[k] = 1.0 / self.prior_gaussian_beta[k] * (\n",
    "                self.prior_gaussian_beta_0[k] * self.prior_gaussian_mean_0[k] + N_k[k] * x_k[k])\n",
    "\n",
    "            W_k_inv = np.linalg.inv(self.prior_wishart_w_0[k]) + N_k[k] * S_k[k] + (self.prior_gaussian_beta_0[k] * N_k[\n",
    "                k]) / (self.prior_gaussian_beta_0[k] + N_k[k]) * np.transpose(\n",
    "                x_k[k] - self.prior_gaussian_mean_0[k]) @ (x_k[k] - self.prior_gaussian_mean_0[k])\n",
    "\n",
    "            self.prior_wishart_w[k] = np.linalg.inv(W_k_inv)\n",
    "\n",
    "            self.prior_wishart_v[k] = self.prior_wishart_v_0[k] + N_k[k]\n",
    "\n",
    "    def fit(self, X):\n",
    "        n_sample, n_feature = X.shape\n",
    "        self.D = n_feature\n",
    "        self._init_params()\n",
    "        last_rst = np.zeros(n_sample)\n",
    "        # 迭代训练\n",
    "        for _ in range(0, self.n_iter):\n",
    "            self._update_single_step(X)\n",
    "            if self.verbose:\n",
    "                utils.plot_contourf(X, lambda x: self.predict_sample_generate_proba(x), lines=5)\n",
    "                utils.plt.pause(0.1)\n",
    "                utils.plt.clf()\n",
    "            current_rst = self.predict_sample_generate_proba(X)\n",
    "            if np.mean(np.abs(current_rst - last_rst)) < self.tol:\n",
    "                break\n",
    "            last_rst = current_rst\n",
    "\n",
    "        if self.verbose:\n",
    "            utils.plot_contourf(X, lambda x: self.predict_sample_generate_proba(x), lines=5)\n",
    "            utils.plt.show()\n",
    "\n",
    "    def predict_proba(self, X):\n",
    "        # 预测样本在几个St上的概率分布\n",
    "        _, D = X.shape\n",
    "        hat_alpha = np.sum(self.prior_dirichlet_alpha)\n",
    "        W = np.asarray([utils.St(X, self.prior_gaussian_mean[k],\n",
    "                                 (self.prior_wishart_v[k] + 1 - D) / (1 + self.prior_gaussian_beta[k]) *\n",
    "                                 self.prior_wishart_w[k] * self.prior_gaussian_beta[k],\n",
    "                                 self.prior_wishart_v[k] + 1 - D) * self.prior_dirichlet_alpha[\n",
    "                            k] / hat_alpha for k in range(0, self.n_components)]).T\n",
    "        W = W / np.sum(W, axis=1, keepdims=True)\n",
    "        return W\n",
    "\n",
    "    def predict(self, X):\n",
    "        # 预测样本最有可能产生于那一个高斯模型\n",
    "        return np.argmax(self.predict_proba(X), axis=1)\n",
    "\n",
    "    def predict_sample_generate_proba(self, X):\n",
    "        # 返回样本的生成概率\n",
    "        _, D = X.shape\n",
    "        hat_alpha = np.sum(self.prior_dirichlet_alpha)\n",
    "        W = np.asarray([utils.St(X, self.prior_gaussian_mean[k],\n",
    "                                 (self.prior_wishart_v[k] + 1 - D) / (1 + self.prior_gaussian_beta[k]) *\n",
    "                                 self.prior_wishart_w[k] * self.prior_gaussian_beta[k],\n",
    "                                 self.prior_wishart_v[k] + 1 - D) * self.prior_dirichlet_alpha[\n",
    "                            k] / hat_alpha for k in range(0, self.n_components)]).T\n",
    "        return np.sum(W, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "测试..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "\n",
    "X, y = make_blobs(n_samples=400, centers=4, cluster_std=0.55, random_state=0)\n",
    "X = X[:, ::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#训练，查看收敛过程可以设置verbose=True\n",
    "gmm = GMMCluster(verbose=False, n_iter=100, n_components=4)\n",
    "gmm.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\app\\Anaconda3\\lib\\site-packages\\matplotlib\\contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15e10f6c8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#查看效果\n",
    "utils.plot_contourf(X,gmm.predict_sample_generate_proba,lines=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15e14eb6518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#查看分类边界\n",
    "utils.plot_decision_function(X,gmm.predict(X),gmm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以发现VI的收敛效果还是不错的，接下来再做一个测试，假如初始的n_components设置很大会怎样"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\app\\Anaconda3\\lib\\site-packages\\matplotlib\\contour.py:967: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15e1539b630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GMMCluster(verbose=False, n_iter=100, n_components=20)\n",
    "gmm.fit(X)\n",
    "utils.plot_contourf(X,gmm.predict_sample_generate_proba,lines=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以发现，上面设置初始聚类中心为20和设置为4的训练结果一样，说明**VI训练的GMM对超参数并不敏感**（这主要是由于引入了先验分布的缘故），所以我们不必再对超参数做交叉验证进行选择了...."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 六.总结一下\n",
    "这一节完整的使用了四个步骤来做GMM的训练，虽然结果还OK，但我们需要更加清晰的认识到一个事实：**如何对隐变量进行拆分，以及假设各变量子集服从何种分布是成功的关键**，如果拆分方式不对，或者分布假设不对可能会取得比较差的结果（并没有做实验去检验...《机器学习》书上的观点）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
